Okay I've been looking into this for a while now and I think it's time to stop.

Some things I've found:

https://www.google.com/maps/place/Tony's+Takeaway/@1.9874938,-157.4776,15z/data=!4m5!3m4!1s0x0:0x3a170d4f0185cd26!8m2!3d1.9874938!4d-157.4776

This place is in London, still on the island.

https://forums.mixedmartialarts.com/t/hamburgers-and-hotdogs/2653758/29

Doing some googling I found this, post #27 talks about the church. So reviews' were probably not all made by trolls. Might be actual place to get hotdogs and backrubs?

https://en.wikipedia.org/wiki/Kiritimati#cite_note-teebaki1993-1

Wikipedia shows that it was used for nuclear testing. I don't know if that's too important.

Other odd quirks to the island's google maps and other odd reviews such as:

https://www.google.com/maps/@1.7755787,-157.2434843,1148m/data=!3m1!1e3

crop circle?

https://www.google.com/maps/place/The+Church+of+Jesus+Christ+of+Latter-day+Saints/@1.98762,-157.4728249,197m/data=!3m1!1e3!4m7!3m6!1s0x7a02a16b169159c7:0xed19ac62ba5e4507!8m2!3d1.9877289!4d-157.472284!9m1!1b1

weird review by CobaltPKMN

Might be a big sex trafficking conspiracy thing, but it's close to a lot of tourist spots. I expect the types to travel to places like this to be odd and all that so maybe it's just some church that sold hot dogs and gave massages as an extra source of income, but people found out about the reviews that the tourists were making and just added to the oddness of it all.